#### Answer

$n=\dfrac{3}{2}$

#### Work Step by Step

Using the properties of equality and combining like terms, the value of the variable that satisfies the given equation, $
7n-10=9n-13
,$ is
\begin{array}{l}\require{cancel}
7n-9n=-13+10
\\\\
-2n=-3
\\\\
n=\dfrac{-3}{-2}
\\\\
n=\dfrac{3}{2}
.\end{array}